Question

given \\(\beta = 32^{\circ}\\) and \\(b = 3\\), determine the following.

a) what is \\(\alpha\\)? round to two decimal places. enter the degree symbol by using the toolbar or typing \deg\.

b) what is \\(a\\)? round to two decimal places.

c) what is \\(c\\)? round to two decimal places.

Explanation:

Find the angle \(\alpha\)

Using the Right Triangle Trigonometry knowledge point

$$ \alpha = 90^\circ - \beta = 90^\circ - 32^\circ = 58^\circ $$

Solve for side \(a\)

Using the Trigonometric Ratios knowledge point

$$
LATEXBLOCK0
$$

Solve for hypotenuse \(c\)

Using the Trigonometric Ratios knowledge point

$$
LATEXBLOCK1
$$

Answer:

a) \(\alpha = 58.00^\circ\) (or \(58^\circ\))

b) \(a \approx 4.80\)

c) \(c \approx 5.66\)